Chapter 10.4, Problem 19E

(a)

To determine

The value of $k$, if at the end of $4$ hour dialysis session, the concentration in the dialysate was $75$ grams per litre and it was rising at the rate of $10$ grams per litre per hour, where $f\left(t\right)$ denotes the concentration of creatinine in the dialysate at time $t$, and it satisfies $y\text{'}=k\left(110-y\right)$.

(b)

To determine

The rate of change of concentration at the beginning of a dialysis and give a justification by comparing with the rate at the end of dialysis, where $k$ is $\frac{2}{7}$.